We present AssistOn-SE, a novel powered exoskeleton for robot-assisted rehabilitation that allows for movements of the shoulder girdle as well as shoulder rotations. Automatically adjusting its joint axes, AssistOn-SE can enable a perfect match between human joint axes and the device axes, not only guaranteeing ergonomy and comfort throughout the therapy, but also extending the usable range of motion for the shoulder joint. Moreover, the adjustability feature significantly shortens the setup time required to attach the patient to the exoskeleton, allowing more effective time be spend on exercises instead of wasting this valuable resource for adjustments. Back-driveable design of AssistOn-SE supports both passive translational movements of the center of glenohumeral joint and independent active control of these degrees of freedom. Thanks to this property, glenohumeral mobilization and scapular stabilization exercises can also be delivered with AssistOn-SE, extending the type of therapies that can be administered using upper-arm exoskeletons. We introduce the design of the exoskeleton and present the kinematic analysis of its self-aligning joint. We also provide implementation details for an early prototype as well as some experimental results detailing range of motion of the device and its ability to track movements of the shoulder girdle.